Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Calculate distances using map scales.
• Interpret floor plans and elevation drawings.
• Use maps to determine routes and estimate travel times.
• Critically evaluate information from maps and plans.
• Calculate costs for home improvements using plans.

Lesson summary

Maps, plans, and other representations are crucial tools for navigating our world and making informed decisions. In South Africa, where diverse geographical landscapes and socio-economic environments exist, the ability to interpret and utilize these representations is vital for personal, community, and national development. This week focuses on equipping you with the necessary skills to critically analyze and apply maps, plans, and other visual aids to solve real-world problems and make sound judgments. From navigating unfamiliar areas to understanding community development plans, these skills are essential for active participation in society.

Lesson notes

2.1 Understanding Map Scales A map scale is the ratio between a distance on a map and the corresponding distance on the ground. It's crucial for determining real-world distances from a map. Map scales can be represented in three ways: Ratio Scale: Expressed as a ratio, e.g., 1:50,

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0. This means 1 unit on the map represents 50,000 of the same units on the ground (e.g., 1 cm on the map represents 50,000 cm on the ground, or 0.5 km).

Word Scale: Stated in words, e.g., "1 cm represents 1 km".

Line Scale (Graphical Scale): A line marked with distances, allowing direct measurement.

Example 1: A map of Gauteng has a scale of 1:250,

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0. The distance between Johannesburg and Pretoria measures 20 cm on the map. What is the actual distance between the two cities in kilometers?

Solution: Scale: 1:250,000, meaning 1 cm on the map = 250,000 cm on the ground.

Distance on map: 20 cm Actual distance in cm: 20 cm 250,000 = 5,000,000 cm Convert cm to km: 5,000,000 cm / 100 cm/m / 1000 m/km = 50 km Therefore, the actual distance between Johannesburg and Pretoria is 50 km.

Example 2: A word scale states: "2 cm represents 5 km". If the distance between two towns on the map is 7 cm, what is the actual distance?

Solution: Scale: 2 cm = 5 km Distance on map: 7 cm Find the km represented by 1cm: 5 km / 2 cm = 2.5 km/cm Actual distance: 7 cm 2.5 km/cm = 17.5 km Therefore, the actual distance between the two towns is 17.5 km. 2.2 Interpreting Floor Plans and Elevation Drawings Floor plans are scaled diagrams showing the layout of a building from above. Elevation drawings show the exterior of a building from a side view.

Key elements include: Walls: Usually shown as thick lines.

Doors and Windows: Indicated by specific symbols.

Rooms: Labeled with names and sometimes dimensions.

Scale: Essential for determining actual room sizes.

Example 3: A floor plan of a house is drawn to a scale of 1:

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0. The living room measures 8 cm by 6 cm on the plan. What are the actual dimensions of the living room in meters? Calculate the area of the living room.

Solution: Scale: 1:50 Length on plan: 8 cm Width on plan: 6 cm Actual length in cm: 8 cm 50 = 400 cm Actual width in cm: 6 cm 50 = 300 cm Convert cm to meters: 400 cm / 100 cm/m = 4 m (Length)

Convert cm to meters: 300 cm / 100 cm/m = 3 m (Width) Area = Length Width = 4m * 3m = 12 square meters. The living room dimensions are 4m x 3m, and the area is 12 m². 2.3 Using Maps for Route Planning and Travel Time Estimation Maps can be used to plan routes and estimate travel times.

Factors to consider include: Distance: Use the map scale to calculate the distance of each route.

Speed: Estimate travel time based on average speed (e.g., using Google Maps estimations, or assuming an average speed). Note that urban and rural areas will have differing average speeds.

Road Conditions: Consider the type of road (highway, gravel road) and potential traffic congestion.

Example 4: You are planning a trip from Durban to Johannesburg using Google Maps. The suggested route is 560 km, and Google Maps estimates the journey will take 6 hours. What is the average speed of the trip? If you decide to take a detour that adds 50 km to the trip, how much longer will the journey take, assuming the same average speed?

Solution: Distance: 560 km Time: 6 hours Average speed: Distance / Time = 560 km / 6 hours = 93.33 km/h (approximately)

New Distance: 560 km + 50 km = 610 km Time = Distance / Speed = 610 km / 93.33 km/h = 6.54 hours (approximately)

Additional time: 6.54 hours - 6 hours = 0.54 hours, or 0.54 60 = 32.4 minutes (approximately) The detour will add approximately 32.4 minutes to the journey. 2.4 Home Improvement Cost Calculations Plans are crucial for home improvements. Understanding the plan allows for accurate material estimation and cost calculation.

Example 5: A homeowner wants to tile their kitchen floor. The floor plan shows the kitchen is a rectangle measuring 3 meters by 4 meters. Tiles cost R120 per square meter. Calculate the total cost of the tiles needed.

Solution: Kitchen dimensions: 3m x 4m Area of kitchen: 3m 4m = 12 square meters Cost per square meter: R120 Total cost: 12 square meters R120/square meter = R1440 The total cost of the tiles needed is R

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0. Guided Practice (With Solutions)

Question 1: A map has a scale of 1:100,

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0. Two cities are 8 cm apart on the map. What is the actual distance between the cities in kilometers?

Solution: Scale: 1:100,000 Map distance: 8 cm Actual distance in cm: 8 cm 100,000 = 800,000 cm Convert cm to km: 800,000 cm / 100 cm/m / 1000 m/km = 8 km Answer: The actual distance between the cities is 8 km.

Commentary: This question directly applies the concept of map scales and unit conversion.

Question 2: A floor plan of a bedroom (scale 1:25) shows a length of 16 cm and a width of 12 cm. What are the actual dimensions of the bedroom in meters?